The effect of classical noise on a quantum two-level system

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Aguilar, Jean-Philippe
Berglund, Nils
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Abstract
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We consider a quantum two-level system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the off-diagonal matrix elements of the Hamiltonian, representing a transverse magnetic field. We determine the invariant measure of the system and prove its uniqueness. In the case of Ornstein-Uhlenbeck noise, we determine the speed of convergence to the invariant measure. Finally, we determine an approximate one-dimensional diffusion equation for the transition probabilities. The proofs use both spectral-theoretic and probabilistic methods.
Comment: 25 pages
Keywords
Mathematics - Probability, Mathematical Physics, 60h10, 35P15, 81Q15, 93E03
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